This works, unlike spell check in evolution. Here’s the path that I used:
gedit → filename → 1st <no name> → 1st <no name> → 1st <no name> → 1st <no name> → 1st <no name> → Tools → Check Spelling → [Take Action]
gedit → Check Spelling → 1st <no name> → 1st <no name> → 1st <no name> → 3rd <no name> → 1st <no name> → Change → [Take Action]